Let A be a complete deterministic finite automaton (DFA) with input alphabet A and state set
Q. We say that such an automaton is synchronising if there exists a word w 2 A such that …

We refine a uniform algebraic approach for deriving upper bounds on reset thresholds of
synchronizing automata. We express the condition that an automaton is synchronizing in …

A set of nonnegative matrices M={M_1,M_2,...,M_k\} is called primitive if there exist possibly
equal indices i_1,i_2,...,i_m such that M_i_1M_i_2⋯M_i_m is entrywise positive. The length …

A survey of the state-of-the-art of the theory of synchronizing automata is given in its part
concerned with the case of complete deterministic automata. Algorithmic and complexity …

We prove that a uniformly random automaton with n states on a 2-letter alphabet has a
synchronizing word of length with high probability (whp). That is to say, whp there exists a …

An automaton is synchronizing when there is a word that brings every state into one and the
same state. Such a word is called a synchronizing word, and Černý conjectured in 1964 that …

Abstract Automata synchronization has many important applications, mostly in conformance
testing of electrical circuits, self-correcting codes and protocol testing. Finding a shortest …

An n-state automaton is synchronizing if it can be reset, or synchronized, into a definite state.
The set of input words that synchronize the automaton is acceptable by an automaton of size …

We present a novel method to predict the length of the shortest synchronizing words of a
finite automaton by applying the machine learning approach. We introduce several so-called …

We study the computational complexity of various problems related to synchronization of
weakly acyclic automata, a subclass of widely studied aperiodic automata. We provide …